In a recent year, the total scores for a certain standardized test were normally distributed, with a mean of 500 and a standard deviation of 10.5. Answer parts (a)-(d) below.
(a) Find the probability that a randomly selected medical student who took the test had a total score that was less than 489 .
The probability that a randomly selected medical student who took the test had a total score that was less than 489 is 0.1474
(Round to four decimal places as needed.)
(b) Find the probability that a randofinly selected medical student who took the test had a total score that was between 497 and 510.
The probability that a randomly selected medical student who took the test had a total score that was between 497 and 510 is
(Round to four decimal places as needed.)
Answer
Final Answer: The probability that a randomly selected medical student who took the test had a total score that was less than 489 is approximately \(\boxed{0.1474}\).
Step 1 ：The problem is asking for the probability of a score being less than 489 in a normal distribution with a mean of 500 and a standard deviation of 10.5.
Step 2 ：This can be solved using the Z-score formula, which is \((X - μ) / σ\), where X is the score, μ is the mean, and σ is the standard deviation.
Step 3 ：The Z-score gives us the number of standard deviations a score is from the mean.
Step 4 ：Substituting the given values into the Z-score formula, we get \((-1.0476190476190477)\).
Step 5 ：We can then use a Z-table to find the probability associated with this Z-score, which is approximately 0.1474.
Step 6 ：Final Answer: The probability that a randomly selected medical student who took the test had a total score that was less than 489 is approximately \(\boxed{0.1474}\).
